Analysis for shear flows past a circular cylinder at low Reynolds number.

Abstract

Analytic solutions for viscous shear flows past a circular cylinder are studied with the Oseen approximation. The governing equation for the velocity field is composed of the equations for the Oseen approximation. The governing equation for the velocity field is composed of the equations for the Oseen velocities and the linear perturbation ones, (uε', v<ε'>), containing the shear parameter`ε'. The latter velocities are evolved from the successive approximation based on the Oseen solution of vorticity. The formal solutions for u of these velocity fields can be written by superimposing the nonsymmetric solutions of the Oseen ones on the above velocities uε'. On the basis of these solutions, the expansion formulas of the stream function, Ψ, and the vorticity, ζ, are respectively obtained up to the fourth powers of the Reynolds number, Re. Flow patterns withε=0.1, 0.16 and 0.5 are shown at Re=0.1. Furthermore, the expansion formulas of lift, moment and pressure distribution are obtained. In the range of Re from 0.01 to 1/0, the value of lift, moment and pressure distribution are obtained. In the range of Re from 0.01 to 1.0, the value of lift gives rise to minus values and these decrease in proportion toε. These results are qualitatively in agreement with ones of numerical solutions whenεis under 0.5.